Uniaxial Extensional Viscosity Research Articles

Predicting maximum strain hardening factor in elongational flow of branched pom-pom polymers from polymer architecture

We present a model-driven predictive scheme for the uniaxial extensional viscosity and strain hardening of branched polymer melts, specifically for the pom-pom architecture, using the small amplitude oscillatory shear mastercurve and the polymer architecture. A pom-pom shaped polymer is the simplest architecture with at least two branching points, needed to induce strain hardening. It consists of two stars, each with q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q$$\\end{document} arms of the molecular weight Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document}, connected by a backbone of Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Despite the pom-pom constitutive model, experimental data of systematic investigations lack due to synthetic complexity. With an optimized approach, we synthesized polystyrene pom-pom model systems with systematically varied Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document} and Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Experimentally, we identify four characteristic strain rate dependent regimes of the extensional viscosity, which can be predicted from the rheological mastercurve. Furthermore, we find that the industrially important maximum strain hardening factor depends only on the arm number by [q2/ln(3q)]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[{q}^{2}/{{{{{\\mathrm{ln}}}}}}({\\sqrt{3}}q)]$$\\end{document}. This framework offers a model-based design of branched polymers with predictable melt flow behavior.

Numerical simulation of fiber orientation kinetics and rheology of fiber-filled polymers in uniaxial extension

During processing of fiber composites, the fiber-induced stresses influence the local flow fields, which, in turn, influence the stress distribution and the fiber orientation. Therefore, it is crucial to be able to predict the rheology of fiber-filled polymer composites. In this study, we investigate the fiber orientation kinetics and rheological properties of fiber composites in uniaxial extensional flow by comparing direct numerical finite element simulations to experimental results from our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. In the simulations, fiber–fiber interactions only occur hydrodynamically and lubrication stresses are fully resolved by using adaptive meshing. We employed a 7-mode and a 5-mode viscoelastic Giesekus material model to describe the behavior of, respectively, a strain hardening low-density polyethylene (LDPE) matrix and a non-strain hardening linear LDPE matrix, and investigated the influence of the Weissenberg number, strain hardening, and fiber volume fraction on the fiber orientation kinetics. We found that none of these parameters influence the fiber orientation kinetics, which agrees with our experimental data. The transient uniaxial extensional viscosity of a fiber-filled polymer suspension is investigated by comparing finite element simulations to a constitutive model proposed by Hinch and Leal [“Time-dependent shear flows of a suspension of particles with weak Brownian rotations,” J. Fluid Mech. 57(4), 753–767 (1973)] and to experimental results obtained in our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. The simulations describe the experimental data well. Moreover, high agreement is found for the transient viscosity as a function of fiber orientation between the model and the simulations. At high strains for high fiber volume fractions, however, the simulations show additional strain hardening, which we attribute to local changes in microstructure.

Does harvesting age matter? Changes in structure and rheology of a shear-thickening polysaccharide from Cyathea medullaris as a function of age

A shear-thickening polysaccharide from the New Zealand Black tree fern (Cyathea medullaris, commonly known as mamaku) extracted from different age fronds (stage 1: young, stage 2: fully grown and stage 3: old) was characterised in terms of structure and rheological properties. Constituent sugar analysis and 1H and 13C NMR revealed a repeating backbone of −4)-β-D-GlcpA-(1 → 2)-α-D-Manp-(1→, for all mamaku polysaccharide (MP) samples from different age fronds without any alterations in molecular structure. However, the molecular weight (Mw) was reduced with increasing age, from ~4.1 × 106 to ~2.1 × 106 Da from stage 1 to stage 3, respectively. This decrease in Mw (and size) consequently reduced the shear viscosity (ηs-Stage 1 > ηs-Stage 2 > ηs-Stage 3). However, the extent of shear-thickening and uniaxial extensional viscosity of MP stage 2 was greater than MP stage 1, which was attributed to a greater intermolecular interaction occurring in the former. Shear-thickening behaviour was not observed in MP stage 3.

Steady-state simulation of the film-casting process for Newtonian and viscoelastic fluids

Thin polymeric films are usually produced in an extensional flow between an extrusion head and a chill roll. The final product is prone to several defects, such as reduced width and non-uniform thickness, and a better understanding of the whole process can improve the final product quality and reduce wastes. This work revisits the film-casting process by exploring the scaling relation between different variables, with particular focus on the width reduction (neck-in). The numerical simulations are carried out for Newtonian, Upper-Convected Maxwell and Giesekus fluids in isothermal and steady-state conditions, for varying film aspect ratio (AR; film width over length), draw ratio (DR) and Deborah number (De). The governing equations are discretized with finite-volumes in their full form (3D model) and using an approximate 2.5D model. However, the latter has been mainly used in this study, as it offered similar accuracy as the 3D model, at a much lower computational cost. The results show that the normalized film shape is independent of the aspect ratio for sufficiently high values of this parameter and that the film thickness scales with DR according to the theoretical prediction for planar and uniaxial extensional flows, in the centre and edge regions, respectively. The neck-in grows logarithmically with the draw ratio for high AR, with a De-dependent growth rate (higher De leads to lower neck-in and lower dependence on DR). There is a reasonable correlation between the neck-in and the ratio between the planar and uniaxial extensional viscosities, as well as between the neck-in and dimensionless variable M = ln(DR)/(De+δ), where δ is a constant which depends on the fluid rheology. However, none of the correlations offer a perfect fit to the neck-in and the search for such a correlation (or master curve) shall be pursued in future works.

Steady elongational flow from rotarance theory

The physics of macromolecular orientation has been used to explain the elasticity of polymeric liquids. Specifically, by first sculpting a rigid bead–rod likeness of the macromolecule, we can then derive its hydrodynamic resistance to orientation. The solution for the orientation distribution function has then been used, by integration in phase space, to get rheological material functions in both (i) small- and (ii) large-amplitude oscillatory shear flow, including its limiting case, and (iii) steady shear flow. However, rheological material functions in steady homogeneous extension from rigid bead–rod theory remain elusive. In this paper, we derive the orientation distribution function, and the rheological material functions, for suspensions of general rigid bead–rod structures. We focus on the time-steady viscosities in extension, and we first do so for general extensional kinematics. We then obtain the viscosities in steady extension for (iv) uniaxial extension, (v) planar extension, and (vi) biaxial extension. We close with a worked example, in which we use our new result for the steady uniaxial extensional viscosity to build a bridge between the macromolecular theory and the Oldroyd framework for rheological constitutive models. We, thus, arrive at a constitutive equation whose parameters are deducible from the moments of inertia of the macromolecule, and thus, deducible from macromolecular architecture alone. Our model is accurate up to third order for time-independent flows and is accurate to second order for time-dependent ones.

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Extensional Rheology of Poly(vinylidene fluoride)/N,N-dimethylformamide Solutions

Typical extension flow occurs in electrospinning process of Poly(vinylidene fluoride) (PVDF) solutions such that researchers focus on extensional rheological behaviors of PVDF solutions. The extensional viscosity of PVDF solutions is measured to know the fluidic deformation in extension flows. The solutions are prepared by dissolving PVDF powder into N,N-dimethylformamide (DMF) solvent. A homemade extensional viscometric device is used to produce uniaxial extension flows and the feasibility of the viscometric device is verified by applying the glycerol as a test fluid. Experimental results show that PVDF/DMF solutions are extension shinning as well as shear shinning. The Trouton ratio of thinning PVDF/DMF solution is close to three at very low strain rate and then reaches a peak value until it drops to a small value at high strain rate. Furthermore, an exponential model may be used to fit the measured values of uniaxial extensional viscosity at various extension rates, while traditional power-law model is applicable to steady shear viscosity. For 10~14% PVDF/DMF solution, the zero-extension viscosity by fitting reaches 31.88~157.53 Pa·s and the peak Trouton ratio is 4.17~5.16 at applied extension rate of less than 34 s-1. Characteristic relaxation time is λ~100 ms and corresponding critical extension rate is ε˙c~5 s-1. The extensional viscosity of very dilute PVDF/DMF solution at very high extension rate is beyond the limit of our homemade extensional viscometric device. This case needs a higher sensitive tensile gauge and a higher-accelerated motion mechanism for test.

Measurement and modeling of uniaxial and planar extensional viscosities for linear isotactic polypropylenes

In this work, novel rectangular and circular orifice (zero-length) dies were used to measure planar and uniaxial extensional viscosities as a function of strain rate for various linear isotactic polypropylene melts by using Cogswell methodology. The obtained experimental data were combined with shear and uniaxial extensional viscosity data determined at very high strain rates. The ability of the molecularized generalized Newtonian fluid (mGNF) [M. Zatloukal and J. Drabek, “Generalized Newtonian fluid constitutive equation for polymer liquids considering chain stretch and monomeric friction reduction for very fast flows modeling,” Phys. Fluids 33(8), 083106 (2021)], Giesekus, and explicit Yao constitutive equations to describe the measured data was tested. It has been shown that including the effect of the chemical environment (i.e., the role of the oligomeric solvent) using a simplified version of the mGNF constitutive equation (instead of the commonly used Newton's law) can significantly improve the ability of the Giesekus and Yao viscoelastic constitutive equations to describe the measured experimental data, especially at very high strain rates with using adjustable parameters with a clear physical meaning.

Effect of viscoelasticity on the foaming behaviour of long-chain branched polypropylene with different branching degrees analysed by using bubble-growth modelling

Long-chain branched polypropylene (LCB-PP) was generated by a melt grafting reaction with trimethylolpropane triacrylate (TMPTA) as the grafting monomer and zinc dimethyldithiocarbamate (ZDMC) or styrene (St) as the co-monomers. High-temperature size exclusion chromatography (HT-SEC) was used to characterize the molecular mass, molecular mass distribution and branching degree of the modified PP. Subsequently, linear and nonlinear viscoelasticity data were obtained by a small amplitude oscillatory shear (SAOS) test and uniaxial extensional viscosity measurement. The pressure balanced bubble-growth (PBB) model was used to calculate the critical coalescence radius (CCR) curves for PP to quantitatively correlate the viscoelasticity and foamability and evaluate the foamability of PP combined with batch foaming. It is shown that with increasing branching degree, the foam shows a better resistance to bubble coalescence, resulting in a more regular bubble structure and a higher expansion ratio. Moreover, viscosity should be controlled over an appropriate range for realising good foamability; otherwise, excessive viscosity can suppress bubble growth and limit the expansion ratio. MPPZ4 modified with 4 wt% TMPTA and 0.4 wt% ZDMC showed the best foamability. A combination of the PBB model and batch foaming experiment is used to quantitatively explain the contribution of LCB to foaming.

Generalized Newtonian fluid constitutive equation for polymer liquids considering chain stretch and monomeric friction reduction for very fast flows modeling

In this work, the recently proposed frame-invariant Generalized Newtonian Fluid (GNF) constitutive equation [M. Zatloukal, “Frame-invariant formulation of novel generalized Newtonian fluid constitutive equation for polymer melts,” Phys. Fluids 32(9), 091705 (2020)] has been modified to provide uniaxial extensional viscosity at a high strain rate limit corresponding to molecular expression for a fully extended Fraenkel chain reported in Ianniruberto et al. [“Melts of linear polymers in fast flows,” Macromolecules 53(13), 5023–5033 (2020)]. It uses basic rheological and molecular parameters together with the ratio of monomeric friction coefficients for equilibrium and fully aligned chains. The modified GNF model was successfully tested by using steady-state uniaxial extensional viscosity data for well-characterized entangled polymer melts and solutions [namely, linear isotactic polypropylenes, poly(n-butyl acrylate), polyisoprenes, and polystyrenes] covering a wide range of strain rates, including those, at which the chain stretch occurs. Only two fitting parameters were sufficient to describe all uniaxial extensional viscosity data, one related to the Rouse stretch time and the other controlling the extensional thinning and thickening behavior at medium and high strain rates. The model was compared to five different advanced viscoelastic constitutive equations, which are based on Doi–Edwards theory and include chain stretch along with a number of important additions. The ability of the proposed GNF model to represent steady uniaxial extensional viscosities under fast flow conditions for entangled polymer fluids has been shown to be superior to the predictions of selected advanced viscoelastic constitutive equations. It is believed that the modified GNF model can be used in the stable modeling of non-Newtonian polymer liquids, especially in very fast steady-state flows where chain stretch begins to occur.

Reduction of monomeric friction coefficient for linear isotactic polypropylene melts in very fast uniaxial extensional flow

For the first time, the monomeric friction coefficient for fully aligned chains, ζaligned, was determined for three linear isotactic polypropylene melts (iPP) using a high-strain-rate limiting value of uniaxial extensional viscosity, ηE,U,∞, obtained from our recent experimental data [Drabek and Zatloukal, Phys. Fluids 32(8), 083110 (2020)] and expression relating ηE,U,∞ with ζaligned, which was derived for a fully stretched Fraenkel chain [Ianniruberto et al., Macromolecules 53(13), 5023–5033 (2020)]. It was found that the obtained ζaligned value is lower by a factor of 2.9–5.0 (or even by a factor of 8.7–16.5 if the effect of polydispersity is included) compared to the equilibrium friction coefficient, ζeq, defined according to Doi and Edwards. This strongly supports recent arguments from rheological data and molecular simulations that a reduction in the friction coefficient must be considered in order to understand dynamics of polymer melts in very fast flows.

Frame-invariant formulation of novel generalized Newtonian fluid constitutive equation for polymer melts

In this work, the frame-invariant formulation of a new generalized Newtonian fluid (GNF) constitutive equation is proposed. Viscosity is considered as a specific function of the second and third invariant of the strain rate tensor and of the second invariant of the objective velocity gradient. The GNF model was successfully tested using experimental data taken from the open literature for different high and low density polyethylene melts with varying amounts of long-chain branches utilizing steady-state shear, uniaxial, and planar extensional viscosities plotted as a function of the strain rate.

Influence of molecular weight, temperature, and extensional rheology on melt blowing process stability for linear isotactic polypropylene

In this work, three linear isotactic polypropylenes with different weight-average molecular weights, Mw, and comparable polydispersities were used to produce nonwovens by melt blowing technology at two different temperatures, T. The air/polymer flow rate was changed to maintain the same average fiber diameter, resulting in a different broadness of fiber diameter distribution, which was quantified by the coefficient of variation, CV. The elasticity of the material was evaluated by the reptation-mode relaxation time, λ1, and the Rouse-mode reorientation time, λ2, determined from the deformation rate dependent shear viscosity data. Extensional rheology was evaluated using uniaxial extensional viscosity measured over a very wide range of strain rates (2 × 104 s−1–2 × 106 s−1) using entrance pressure drop and Gibson methods. An obtained plateau value of uniaxial extensional viscosity at the highest extensional strain rates, ηE,∞ (normalized by the three times zero-shear rate viscosity, η0), and the minimum uniaxial extensional viscosity, ηE,min, were related to Mw and T using simple equations. It has been found that the stability of fiber production captured by CV depends exclusively on the extensional properties of the polypropylene melts, namely, ηE,U,∞3η0 and ηE,U,min. These findings are important especially with regard to the stable production of polymeric nanofibers by melt blowing technology.

Rheological measurement of the nonlinear viscoelasticity of the ABS polymer and numerical simulation of thermoforming process

The thickness distribution of thermoformed products is greatly affected by the viscoelastic behavior of the extruded polymer sheet. In this work, linear and nonlinear rheological experiments are carried out to characterize the viscoelastic properties of acrylonitrile-butadiene-styrene sheets under thermoforming conditions including a wide range of temperatures, strains, and strain rates. First, aspects of linear viscoelasticity such as the storage modulus and loss modulus are measured by small-amplitude oscillatory shear experiments. The discrete relaxation spectra and the Williams-Landel-Ferry parameters are obtained from the constructed linear master curves. Then, nonlinear time-dependent extensional viscosity is measured by uniaxial extensional experiments. The parameters of the damping function are evaluated using an optimization method. In addition, the effect of the orientation of the polymer is analyzed. The uniaxial extensional stress and viscosity in the extruder direction demonstrate higher resistance against tearing and extreme thickness reduction during processing. Finally, the linear and nonlinear input parameters for the numerical simulation are prepared. Numerical simulations are performed using the Wagner model with the obtained nonlinear viscoelasticity. The thickness distribution in thermoformed ABS sheets, obtained numerically, shows good agreement with the experimentally obtained values.

Uniaxial extensional viscosity of semidilute DNA solutions

The extensional rheology of polymeric liquids has been extensively examined through experiments and theoretical predictions. However, a systematic study of the extensional rheology of polymer solutions in the semidilute regime, in terms of examining the effects of concentration and molecular weight, has not been carried out so far. Prior studies of the shear rheology of semidilute polymer solutions have demonstrated that their behaviour is distinctively different from that observed in the dilute and concentrated regimes. This difference in behaviour is anticipated to be even more pronounced in extensional flows. In this work, the extensional rheology of linear, double-stranded DNA molecules, spanning an order of magnitude of molecular weights (25 to 289 kilobasepairs) and concentrations (0.03 to 0.3 mg/ml), has been investigated. DNA solutions are now used routinely as model polymeric systems due to their near-perfect monodispersity. Measurements have been carried out with a filament stretching rheometer since it is the most reliable method for obtaining an estimate of the elongational stress growth of a polymer solution. Transient and steady-state uniaxial extensional viscosities of DNA dissolved in a solvent under excess salt conditions, with a high concentration of sucrose in order to achieve a sufficiently high solvent viscosity, have been determined in the semidilute regime at room temperature. The dependence of the steady state uniaxial extensional viscosity on molecular weight, concentration and extension rate is measured with a view to determining if data collapse can be observed with an appropriate choice of variables. Steady state shear viscosity measurements suggest that sucrose-DNA interactions might play a role in determining the observed rheological behaviour of semidilute DNA solutions with sucrose as a component in the solvent.

Ray Fernando wins 2019 Tess Award

Ray Fernando is the winner of the 2019 Roy W. Tess Award in Coatings, sponsored by the American Chemical Society Division of Polymeric Materials: Science and Engineering. Fernando is the Arthur C. Edwards Endowed Chair and the director of the Polymers and Coatings Program in the Chemistry and Biochemistry Department at California Polytechnic State University, San Luis Obispo. The $3,000 award recognizes outstanding contributions to coatings science, engineering, and technology. Fernando has made important contributions to understanding the role of dynamic uniaxial extensional viscosity in properties like spatter of roller-applied coatings that dominate the architectural market, as well as the behavior of spray-applied waterborne coatings used extensively in industrial applications. He received the award during the fall ACS national meeting in San Diego. Please send announcements of awards to l_wang@acs.org.

Shock wave emission and cavitation bubble dynamics by femtosecond optical breakdown in polymer solutions.

Shock wave emission and the dynamics of micrometer-sized cavitation bubbles generated after femtosecond optical breakdown in viscoelastic fluids were investigated experimentally using high-speed photography with 5 million frames/s and acoustic measurements. The viscoelastic fluids consisted in a 0.5% polyacrylamide solution, with a strong elastic component, and a 0.5% carboxymethylcelullose, with a weak elastic component. Breakdown in water and both polymer solutions generated a purely compressive pressure wave. The maximum amplitude and the duration of the breakdown shock wave as well as the maximum bubble radius were not affected by the polymer additives. The notable influence of the polymer additives was found during the collapse phase of the bubble and is manifested by a prolongation of the oscillation time of the bubble and a reduction of the maximum pressure of the shock wave emitted during bubble collapse. A sizeable attenuation of the bubble collapse was found in the elastic polyacrylamide solution. The present results are consistent with an interpretation which invokes the effect of enhanced levels of uniaxial extensional viscosity on the collapse of micrometer-sized cavitation bubbles. The consequences for cavitation in blood are also discussed.

Influence of long chain branching on fiber diameter distribution for polypropylene nonwovens produced by melt blown process

In this work, linear isotactic polypropylene (L-PP) and long-chain branched polypropylene (LCB-PP) miscible blend, both having comparable weight average molecular weight, zero-shear viscosity, and polydispersity index, were used to produce nonwovens via melt blown technology in order to understand the role of long chain branching in the fiber diameter distribution. Basic morphological characteristics of produced nonwoven samples have been determined using digital image analysis of scanning electron microscope images considering different magnifications to capture nanofibers as well as microfibers. At the same air flow rate, polymer flow rate, and temperature, the average fiber diameters were the same, 1.6 μm, but the coefficient of variation, CV, was greater for the linear PP than for the blend. Material elasticity was assessed by reptation-mode relaxation time, λ, determined by fitting of deformation rate dependent shear viscosity by Cross and Carreau-Yasuda models as well as via fitting of frequency dependent loss and storage moduli master curve by a two-mode Maxwell model. It was found that λ is higher for LCB-PP in comparison with L-PP and the Cross model gives a meaningful relaxation time while the Carreau-Yasuda model does not despite giving a better numerical fit. Extensional rheology was assessed by the strain rate dependent uniaxial extensional viscosity (estimated from the entrance pressure drop using the Gibson method). The infinite shear to zero-shear shear viscosity ratio η∞/η0 (obtained directly from the shear viscosity data measured in a very wide shear rate range) was shown to be proportional to the maximum normalized extensional viscosity at very high extensional strain rates, ηE,∞/(3η0). η∞/η0 was related to temperature and basic molecular characteristics of given polymers via simple equation. It was observed that extensional viscosity for both samples first decreases with increased extensional strain rate to its minimum value at 200 000–400 000 1/s and then increases to plateau value, ηE,∞ (corresponding to the maximum chain stretch) at about 2 ⋅ 106 1/s. At low deformation rates, extensional viscosity is higher for LCB-PP in comparison with L-PP, but the trend is switched at very high deformation rates; ηE,∞ (and also ηE,∞/3η0) becomes lower for LCB-PP in comparison with L-PP. These results suggest that high stability of LCB-PP blend can be explained by its higher stretchability at very high deformation rates (occurring at the die exit where an intensive fiber attenuation takes the place) and its lower stretchability at medium and low deformation rates, at which melt/air inertia driven bending instability called whipping occurs.

Molecular continua for polymeric liquids in large-amplitude oscillatory shear flow

In this paper, we connect a molecular description of the rheology of a polymeric liquid to a continuum description, and then test this connection for large-amplitude oscillatory shear (LAOS) flow. Specifically, for the continuum description, we use the 6-constant Oldroyd framework, and for the molecular, we use the simplest relevant molecular model, the suspension of rigid dumbbells. By relevant, we mean predicting at least higher harmonics in the shear stress response in LAOS. We call this connection a molecular continuum, and we examine two ways of arriving at this connection. The first goes through the retarded motion expansion, and the second expands each of a set of specific material functions (complex, steady shear, and steady uniaxial extensional viscosities). Both ways involve in comparing the coefficients of expansions and then solve for the six constants of the continuum framework in terms of the two constants of the rigid dumbbell suspension. The purpose of a molecular continuum is that many well-known results for rigid dumbbell suspensions in other flow fields can also be easily obtained, without having to firstly find the orientation distribution function. In this paper, we focus on the recent result for the rigid dumbbell suspension in LAOS. We compare the accuracies of the retarded motion molecular continuum (RMMC) with the material function molecular continuum (MFMC). We find the RMMC to be the most accurate for LAOS.

On the role of extensional rheology and Deborah number on the neck-in phenomenon during flat film casting

In this work, viscoelastic, isothermal extrusion film casting simulations have been performed utilizing a 1D membrane model and the viscoelastic modified Leonov model as the constitutive equation in order to elucidate the role of planar to uniaxial extensional viscosity ratio, extensional strain hardening and Deborah number on the neck-in phenomenon. Based on the performed theoretical parametric study, it has been found that neck-in can be correlated to all the above mentioned variables via a simple dimensionless analytical equation. This correlation can provide detailed view into the complicated relationship between polymer melt rheology, die design, process conditions and undesirable neck-in phenomenon. Obtained results have been validated against literature experimental data for different polyethylene melts and processing conditions.